Select the correct answer.

A 46.9 gram sample of a substance has a volume of about 3.5 centimeters [tex]^3[/tex]. It is solid at a room temperature of [tex]23^{\circ} C[/tex]. Out of the four substances whose properties are given, which is the most likely identity of this substance?

\begin{tabular}{|l|c|c|c|}
\hline
\multicolumn{1}{|c|}{Substance} & \begin{tabular}{c}
Density \\
[tex]$\left( g / cm^3 \right)$[/tex]
\end{tabular} & \begin{tabular}{c}
Melting \\
Point [tex]$\left({ }^{\circ}C \right)$[/tex]
\end{tabular} & \begin{tabular}{c}
Boiling \\
Point [tex]$\left({ }^{\circ}C \right)$[/tex]
\end{tabular} \\
\hline
molybdenum & 10.28 & 2,623 & 4,639 \\
\hline
mercury & 13.53 & -39 & 357 \\
\hline
hafnium & 13.31 & 2,233 & 4,603 \\
\hline
lead & 11.34 & 327 & 1,749 \\
\hline
\end{tabular}

A. molybdenum
B. mercury
C. hafnium
D. lead



Answer :

To identify the most likely substance given the data, let's follow these steps:

1. Given Data:
- Mass of the substance: [tex]\( 46.9 \)[/tex] grams
- Volume of the substance: [tex]\( 3.5 \)[/tex] cm[tex]\(^3\)[/tex]
- Temperature: [tex]\( 23^\circ \)[/tex]C (room temperature)

2. Calculate the Density of the Unknown Substance:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{46.9 \, \text{grams}}{3.5 \, \text{cm}^3} = 13.4 \, \text{g/cm}^3 \][/tex]

3. Compare with Given Densities for Different Substances:
- Density of molybdenum: [tex]\( 10.28 \, \text{g/cm}^3 \)[/tex]
- Density of mercury: [tex]\( 13.53 \, \text{g/cm}^3 \)[/tex]
- Density of hafnium: [tex]\( 13.31 \, \text{g/cm}^3 \)[/tex]
- Density of lead: [tex]\( 11.34 \, \text{g/cm}^3 \)[/tex]

4. Find the Closest Density:
- The calculated density of the unknown substance is [tex]\( 13.4 \, \text{g/cm}^3 \)[/tex].
- Comparing this with the given densities:
- The density of molybdenum: [tex]\( 10.28 \, \text{g/cm}^3 \)[/tex] is quite different from 13.4 g/cm[tex]\(^3\)[/tex].
- The density of mercury: [tex]\( 13.53 \, \text{g/cm}^3 \)[/tex] is close but not as close as hafnium.
- The density of hafnium: [tex]\( 13.31 \, \text{g/cm}^3 \)[/tex] is very close to 13.4 g/cm[tex]\(^3\)[/tex].
- The density of lead: [tex]\( 11.34 \, \text{g/cm}^3 \)[/tex] is also quite different from 13.4 g/cm[tex]\(^3\)[/tex].

Therefore, the closest match in terms of density is hafnium.

5. Room Temperature Consideration:
- While mercury has a density close to [tex]\( 13.4 \, \text{g/cm}^3 \)[/tex], it is liquid at [tex]\( 23^\circ \)[/tex]C because its melting point is [tex]\(-39^\circ \)[/tex]C.
- Hafnium, having a melting point of [tex]\( 2,233^\circ \)[/tex]C, remains solid at [tex]\( 23^\circ \)[/tex]C.

Therefore, taking into consideration both the density and the state of the substance at room temperature, the most likely identity of the substance is:

C. hafnium